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Lera25 [3.4K]
1 year ago
13

Simplify the trigonometric expression. sin4(α) − cos4(α) + cos2(α)

Mathematics
1 answer:
natulia [17]1 year ago
5 0

Answer:

sin²(α)

Step-by-step explanation:

sin⁴(α) − cos⁴(α) + cos²(α)

sin⁴(α) − cos²(α) (cos²(α) − 1)

sin⁴(α) − cos²(α) (-sin²(α))

sin⁴(α) + sin²(α) cos²(α)

sin²(α) (sin²(α) + cos²(α))

sin²(α) (1)

sin²(α)

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A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between
Tju [1.3M]

The Set Up:

x² = (Side1)² + (Side2)² - 2[(Side1)(Side2)]

Solution:

cos(Toby's Angle) • x² = 55² + 65² - 2[(55)(65)] cos(110°)

x² = 3025 + 4225 -7150[cos(110°)]

x² = 7250 - 2445.44x =

√4804.56x = 69.31m

The distance, x, between two landmarks is 69.31m.

Note: The answer choices given are incorrect.

3 0
1 year ago
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Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −2y2 + 6y = −2
andrezito [222]
-2y^2 + 6y + 2 = 0
a = -2, b = 6, c = 2
x = (- b + - sqrt(b^2-4ac))/(2a)
x=(-6+-sqrt(36-4*-2*2))/-4
x=(-6+-sqrt(36+16))/-4
x=(-6+-sqrt(52))/-4
x = (-6 +- 2sqrt13)/-4
x = (3 + - sqrt13)/2
8 0
2 years ago
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Which of the following are terms in the sum of the given polynomials? 3x2,-2x2y, 2xy2, 4y2, xy2, -y2,2x2y
vampirchik [111]
Create the sum of the given polynomial terms.
f(x,y) = 3x² - 2x²y + 2xy² + 4y² + xy² - y² + 2x²y
        = 3x² + 3xy² + 3y²

Test the given terms to see if they belong in f(x,y).
3:       NO
3x²:   YES
3y²:   YES
3xy²: YES
4x²:   NO

Answer:
The terms in the sum of the given polynomials are 3x², 3y², and 3xy².

6 0
2 years ago
Which equations have the variable term in the equation 6 + 2x = 6x - 9 isolated to one side of the equals sign, and
MrRissso [65]

Answer:

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3 = 4x

7 0
1 year ago
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Each of four students hands in a homework paper. Later the teacher hands back the graded papers randomly, one to each of the stu
Stella [2.4K]

Answer:

9 possible ways.

Step-by-step explanation:

To explain this problem i'm going to use letters and numbers (only as example). The letters correspond to a student and the numbers to a homework. Te correct form we have is:

<u>Student</u> ⇒ <u>Homework</u>

    A       ⇒    1

    B       ⇒    2

    C       ⇒    3

    D       ⇒    4

In how many ways can the papers be handed back such that every student receives someone else's paper?. To answer this we need to form every group of Student/Homework possible, but not taking into count the correct way (showing above)

Possible groups:

1) A-2/B-1/C-4/D-3

2)A-2/B-4/C-1/D-3

3)A-2/B-3/C-4/D-1

4)A-3/B-1/C-4/D-2

5)A-3/B-4/C-2/D-1

6)A-3/B-4/C-1/D-2

7)A-4/B-1/C-2/D-3

8)A-4/B-3/C-2/D-1

9)A-4/B-3/C-1/D-2

We have 9 possible ways,

3 0
2 years ago
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